The Deep Symbolism of the Mobius Strip

The Mobius Strip

If ever there was something which merited the name “God” in my eyes, it would be the Mobius Strip. But I don’t believe in a personal, let-alone sentient, god. I’d be far more inclined to call it “Tao” instead. Buddhists might call it “Om” (or “Aum”). Mathematicians should call it “i” (the square root of negative one), but there are even more examples in Mathematics (the involution, the half-rotation, inconsistency, contradiction, “not” or the symbol ¬). Electronics circuits represent it as the inverter whose ouput feeds back into its input. Philosophers might call it “contradiction” or more formally the “paradox of self-reference” epitomized in the Liar Paradox:

“This statement is False.”
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The Present is “Not” – a Transformation Ontology

When you think about transformations, how they exist ‘en soi’ (they are, independent of origin or basis) because to exist is to be different, and to be different is to transform (or be a transformation), and given that Matter is, ultimately, Immaterial ‘Energy’ – which is just another word for transformation (even ‘potential’ energy is just self-cancelling transformations – two collinear but anti-directional vectors of identical magnitude are ‘potential’ vectors, which, if either is ‘rotated’ so that they are no longer collinear, thereby become ‘actual’ vectors, kinetic energy).

As I’ve said elsewhere, the first, ‘basest’ or most ‘atomic’ transformation is the zero-dimensional ‘reflection’, which we humans call “not” – i.e. the logical negation/inversion. This transformation is physically imperceptible to us except in one dimensions – a Rotation. Leptons ‘have’ spin. I’d go even so far as to say they are spin. Even neutrinos are said to “have half-integer spin” –Wikipedia.

But even the ‘self’ is a zero-dimensional ‘reflection’ defined as ‘not’ (“I am not my reflection” or “I am not you”). Thoughts, though I haven’t actually done this yet – but intend to – may well be ‘representable’ as transformations also. If so, they arguably ‘are’ transformations. This is contentious and I’m more than willing to work more on this! Though I am by far not the only one to think of this – just look at Douglas Hofstadter’s “I am a Strange Loop”.

And even further (and this one makes me uneasy), the Present, our ‘now’, is the boundary between Past and Future, and being ‘not’ either one, can be conceived as the transformation (reflection) of the future into the past. Like a single half-twist in a strip of paper travelling along it, what’s ahead is the ‘potential’ future – i.e. ‘unknown sameness’, ‘self-cancelling transformations’ – ‘potential energy’. What is behind the twist is the past, also ‘unknown sameness’, or ‘self-cancelling transformations’ – but being subjected to a reflection, it is forever ‘not’ the future. If the future is ‘zero’ (a digital analogy), then the past is ‘one’. And the present is the transformation ‘effecting’ the past.

All of reality can be broken down to transformations, and the very essence of Time – the quality of temporality – is expressed in the ‘liar’s paradox’ aspect of a self-reflecting ‘not’: “This statement is False (‘not’ true)” can be expressed as a recursive inversion x=-1/x, which resolves into x2=−1 – i.e. the mathematical constant ‘i’. “i” expresses a rotation just as -1 expresses a reflection (where a reflection in a given dimension is a rotation of 180° through a higher dimension). The ‘irresolvability of i’ is temporality. The ‘direction’, or historicity of Time arises in the irrevocable transformation of future into past (where past is not-future and future is not-past).

The past does not ‘exist’ – it has existed. The future does not ‘exist’ – it has not existed. Only the present ‘exists’ because it is the ‘act of existence’ itself – a transformation.

Finally, the old subject-object dilemma is resolved/united via that strange transformation “not” – the subject is not the object; the observer is not the observed. The interaction between the two happens via the reflection “not”. This harps back to the quantum-mechanics problem of the ‘observer effect’ (see the “Quantum Mechanics” sub-heading in this Wikipedia article).

I’m really sorry, but I just can’t make peace with how all-encompassing this damned transformation is! It’s freaking everywhere, and yes, I am aware this smacks of confirmation bias… but I can’t help it! Which is why I need your help. How viable is all of this? Is this utterly nuts? Think about it and get back to me, please!

Thank you for reading.

Look again! Law of Paradox is True…

This is my most risky post. This is one of those posts I know will peg me as mad, but will turn out to be true, if only someone were to come along later and maybe re-word it so that it is more palatable to a wider audience. So here goes…

Much of philosophy is dependent upon three laws – what are called the three laws of formal ontology:

  • The Law of Identity (ID). It states “That which is, is.”
  • The Law of the Excluded Middle (EM). It states “Everything either is or is not.”
  • The Law of Non-contradiction (NC) (also strangely called the Law of Contradiction). It states “Nothing can both be and not be.”

I will show you that the last law (NC) is a contradiction in itself, and by being so, admits the validity of paradox.

But first, some ‘ground rules’ or tools with which to break down the three laws:

  • Truth:
    • Take to be True that which is permanent, which ‘hold still’. Truth forever is True.
  • Falsity:
    • Take to be False that which is not permanent, that which does not ‘hold still’. Falsity is never (not forever) True.
  • Not:
    • The inverse of ‘is’, where ‘is’ is ‘not-not’. So, ‘not’, on its own, is of similar quality to False, because it is unstable, undeterminable, and can never ‘hold’. All odd numbers of ‘nots’ are identical to a single ‘not’.
  • Is:
    • The inverse of ‘not’, or not ‘not’. ‘Not-not’, is of similar quality to True, because it is, stable and determinable, and will forever ‘hold’. All even numbers of ‘not’s are identical to a double ‘not’ –> ‘not-not’.
  • Or:
    • This is ‘not’, in the sense of ‘one, not the other’, this is a part, a disjunction, as per above False.
  • And:
    • This is not ‘Or’, or ‘not-not’, in the sense ‘Not(one not the other)’, this is the rejection of the part, acceptance of the whole, a conjunction, as per above True.
  • All:
    • That which exists and that from which is existed, both Thing and not-Thing. “Is and is not” which is ‘not-not not-not not-not not’, which is False, forever changing and unpredictable and cannot hold still.
  • Thing:
    • A ‘thing’ is what is, that which stands-out from the All, i.e. that which is not-All. Thing evaluates to “not-All”, so one more ‘not’, and so evaluates to ‘not-not’. True.
  • Nothing:
    • That which is not-Thing, i.e. “not not-All” – where ‘not-not’ is, so “Nothing is All”. Nothing == All. Nothing has the same qualities as All and as Falsity, it is forever changing and unpredictable and cannot hold still. False.

 

Now let us look at these laws:

The Law of Identity: “That which is, is.”

  • “That which is”, is “Thing” as per above. Thing is ‘not-not’.
  • “Is”, we’ve seen, is ‘not-not’.

Rebuilding this statement, we have “Thing is”: ‘not-not not-not not-not’: ID is True.

 

The Law of the Excluded Middle: “Everything either is or is not.”

  • “Everything” is ‘every (single) thing’. We can thus consider just one ‘thing’ and consider its truth to be applicable to every one of them. Thing is ‘not-not’.
  • “Either” is superfluous to “or”, so we can rephrase it to “Everything is or is not.”
  • “Is”, we’ve seen, is ‘not-not’.
  • “Or”, above, is ‘not’.
  • “Is not”, is ‘not-not not’.

Rebuilding this statement, we have “Thing is or is not”: ‘not-not not-not not not-not not’ – eight ‘nots’, which is True. EM is True.

 

The Law of Non-Contradiction: “Nothing can both be and not be.”

  • “Nothing” is ‘No Thing’, is not Thing, is ‘not not-All’, is ‘is All’, evaluates to ‘not-not-not’.
  • “Can”, is permission, so is equivalent to “is”, ‘not-not’.
  • “Both” is superfluous to ‘and’, just as ‘either’ was superfluous to ‘or’.
  • “Be” is “is”, ‘not-not’.
  • “And”, as above, is “is”, ‘not-not’
  • “Not be” is not “Be”, is not “is”, is “is not”, ‘not-not-not’.

Rebuilding the statement, we have “Nothing is and is not”: ‘not-not-not not-not not-not not-not-not’ – ten ‘nots’, which is True.

 

But let’s look at that last one (NC) again: We’ve seen that Nothing is All. So “All can both be and not be” This is a permissive statement indicating that A=¬A, a paradox! How can the Law of Non-Contradiction contradict itself?!? Because it admits paradox! At every moment, we remain coherent, even though it sounds so strange: “Nothing is and is not” <–> ”All is and is not”<–> ”All is True and False” (which, finally, is of vital importance if we’re to even have a concept of Truth, because there can be no Truth without what is not-True). This only admits that our Reality allows for the existence of Paradox (which, when you think about it, makes sense A) because we’ve got a name for it: Paradox, and B) we’re a part of this Reality, and we can conceive of Paradox, and C) it is a truly pesky thing which keeps cropping-up whenever mathematicians try to formalize the logic of the fundamentals of mathematics – paradox doesn’t go away!).

All, some may argue is not Nothing. But when you take Everything, and remove all boundaries between every Thing, you are left with a masse whole with no Thing – which is the apeiron – the All with out limit.